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Please solve a through d.
At t 0, an ensemble of particles is in the state...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of th...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
At time t = 0 a particle in a Harmonic Oscillator potential is in the state...
At time t = 0 a particle in a Harmonic Oscillator potential is in the state plcx.e = 0) = va (23*43+(iv]+213) por mayorale * a. Find the expectation value of the momentum (p). b. What is the probability of measuring the state to have energy E = 9ħw/2? E = 3ħw/2? c. Find y(x, t).
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to e...
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
A harmonic oscillator is in a state such that a measurement of the energy would yield...
A harmonic oscillator is in a state such that a measurement of the energy would yield either Eo=(1/2ho 1/3 of the time or E1-(3/2)hw, 2/3 of the time time-dependent wave function which describes this state. (b) Find the average position of the particle (x(t)). (c) Find the expectation value of the energy. Given that E(H), is the energy associate with this state constant or it oscillates in time between Eo and E1?
Please solve question 3 ,4,5,6 the state IL,tni is an eigenvestor of i and izg with...
Please solve question 3 ,4,5,6
the state IL,tni is an eigenvestor of i and izg with eigeanvalues of +1) and mzh, respectively. Find L>and<I2> n electron is placed in a uniform magnetic field B Bok. At time t O S, was measured and was found to be h/2. (a) (5 points) Write its spin wavefunction at any later time t. (b) (5 points) Calculate < S () (5 pointa) At what time t if you mensure the y component of...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p.
[4] Consider a harmonic oscillator...
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscill
5. A particle in the harmonic oscillator potential has the initial wave function Psi(x, 0) = A[\psi_{0}(x) + \psi_{1}(x)] for some constant A. Here to and ₁ are the normalized ground state and the first excited state wavefunctions of the harmonic oscillator, respectively. (a) Normalize (r, 0). (b) Find the wavefunction (r, t) at a later time t and hence evaluate (x, t) 2. Leave your answers involving expressions in to and ₁. c) sing the following normalized expression of...
A particle in the harmonic oscillator potential, V(x) - m2t2, is at time t 0 in...
A particle in the harmonic oscillator potential, V(x) - m2t2, is at time t 0 in the state ψ(x, t-0) = A3ψο(x) +4ψι (2)] where vn (z) is the nth normalized eigenfunction (a) Find A so that b is normalized. (b) Find ψ(x,t) and |ψ(x, t)12 (c) Find x (t) and p)(t). what would they be if we replaced ψ1 with V2? (hint: no difficult calculations are required) Check that Ehrenfest's theorem (B&J 3.93) holds for this wavefunction. (d) What...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harm...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
(30) 1. a) Briefly explain the physical reasoning for requiring a wavefunction to be normalized, b)...
(30) 1. a) Briefly explain the physical reasoning for requiring a wavefunction to be normalized, b) The state of a harmonic oscillator is given by the wavefunction: P(x, t0) = A1 01(x) + A2 02(x). Where Al and A2 are constants and 1(x) and 02(x) are energy eigenfunctions associated with energies E, and E. What condition must A1 and A2 satisfy in order for 'Plx, t0) to be normalized? c) If the particle in the state P(x,t=0), given above, is...
A particle with mass m is in a one dimensional simple harmonic oscillator potential. At timet0 it is described by the superposition state where Vo, 1 and Vz are normalised energy eigenfunctions of the harmonic oscillator potential corresponding to energies Eo, E1 and E2 (a) Show that the wavefunction is normalised (b) If an observation of energy is made, what is the most likely value of energy and with what probability would it be obtained? (c) If the experiment is...
At time t = 0 a particle in a Harmonic Oscillator potential is in the state plcx.e = 0) = va (23*43+(iv]+213) por mayorale * a. Find the expectation value of the momentum (p). b. What is the probability of measuring the state to have energy E = 9ħw/2? E = 3ħw/2? c. Find y(x, t).
A particle with mass m is in a one-dimensional simple harmonic oscillator potential. At time t = 0 it is described by the state where lo and l) are normalised energy eigenfunctions corresponding to energies E and Ey and b and c are real constants. (a) Find b and c so that (x) is as large as possible. b) Write down the wavefunction of this particle at a time t later c)Caleulate (x) for the particle at time t (d)...
A harmonic oscillator is in a state such that a measurement of the energy would yield either Eo=(1/2ho 1/3 of the time or E1-(3/2)hw, 2/3 of the time time-dependent wave function which describes this state. (b) Find the average position of the particle (x(t)). (c) Find the expectation value of the energy. Given that E(H), is the energy associate with this state constant or it oscillates in time between Eo and E1?
Please solve question 3 ,4,5,6
the state IL,tni is an eigenvestor of i and izg with eigeanvalues of +1) and mzh, respectively. Find L>and<I2> n electron is placed in a uniform magnetic field B Bok. At time t O S, was measured and was found to be h/2. (a) (5 points) Write its spin wavefunction at any later time t. (b) (5 points) Calculate < S () (5 pointa) At what time t if you mensure the y component of...
[4] Consider a harmonic oscillator of mass m and angular frequency ω. At time t-0, the state of this oscillator is given by y(о) со фо) + с ф.) where the states I 0) .) represent the ground state and first excited state respectively. (a) Write the normalization condition for lv(o) and determine the mean value (H) of the energy in terms of co and ci. (b) With the additional requirement (H)-ho. calculate eoand o,p.
[4] Consider a harmonic oscillator...
A particle in the harmonic oscillator potential, V(x) - m2t2, is at time t 0 in the state ψ(x, t-0) = A3ψο(x) +4ψι (2)] where vn (z) is the nth normalized eigenfunction (a) Find A so that b is normalized. (b) Find ψ(x,t) and |ψ(x, t)12 (c) Find x (t) and p)(t). what would they be if we replaced ψ1 with V2? (hint: no difficult calculations are required) Check that Ehrenfest's theorem (B&J 3.93) holds for this wavefunction. (d) What...
1. Consider a spin-0 particle of mass m and charge q moving in a symmetric three-dimensional harmonic oscillator potential with natural frequency W.Att-0 an external magnetic field is turned on which is uniform in space but oscillates with temporal frequency W as follows. E(t)-Bo sin(at) At time t>0, the perturbation is turned off. Assuming that the system starts off at t-0 in the ground state, apply time-dependent perturbation theory to estimate the probability that the system ends up in an...
(30) 1. a) Briefly explain the physical reasoning for requiring a wavefunction to be normalized, b) The state of a harmonic oscillator is given by the wavefunction: P(x, t0) = A1 01(x) + A2 02(x). Where Al and A2 are constants and 1(x) and 02(x) are energy eigenfunctions associated with energies E, and E. What condition must A1 and A2 satisfy in order for 'Plx, t0) to be normalized? c) If the particle in the state P(x,t=0), given above, is...
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